The degrees of onesided resolvingness and the limits of onesided resolving directions for endomorphisms and automorphisms of the shift

摘要

We introduce the notions in the title for endomorphisms of subshifts, andusing them we characterize various classes of "resolving endomorphisms ofsubshifts" in the broad sense including onesided and weak ones. Resolvingendomorphisms of transitive topological Markov shifts and resolvingautomorphisms of topological Markov shifts are treated particularly in detail.Moreover, we understand what the limits of onesided resolving directions arefor "expansiveness" (in the broad sense including onesided ones) ofendomorphisms of subshifts, and we understand the relation between"resolvingness" and "expansiveness" for endomorphisms and automorphisms ofsubshifts and for Z^d-actions on zero-dimensional compact metric spaces.